## Abstract

The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k-subdivision denoted by S_{k} (G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs S_{k} (G), specifically for some special graphs, those are path graph (P_{n}), cycle graph (C_{n}), complete graph (K_{n}), star graph (S_{n}), ladder graph (L_{n}), book graph (B_{n}), wheel graph (W_{n}) and fan graph (F_{n}).

Original language | English |
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Article number | 012015 |

Journal | Journal of Physics: Conference Series |

Volume | 1494 |

Issue number | 1 |

DOIs | |

Publication status | Published - 27 May 2020 |

Event | Soedirman''s International Conference on Mathematics and Applied Sciences 2019, SICoMAS 2019 - Purwokerto, Indonesia Duration: 23 Oct 2019 → 24 Oct 2019 |